Given:
f(x) = root x - 5
Rewrite the function using y,
[tex]y=\sqrt[]{x}-5[/tex]Now, interchange the position of x and y in the function,
[tex]x=\sqrt[]{y}-5[/tex]Isolate the dependent variable
[tex]\begin{gathered} \sqrt[]{y}=x+5 \\ y=(x+5)^2 \end{gathered}[/tex]Therefore,
[tex]f^{-1}(x)=(x+5)^2[/tex]And the domain is minus infinity to infinity
[tex]\begin{gathered} f^{-1}(x)=(x+5)^2 \\ \text{Domain}=(-\infty,\infty) \end{gathered}[/tex]Determine if the following answers are true or false. If false, justify why it’s not true and find the correct answer(s). If true, justify why they are correct. You must show your step-by-step process to solve each question to receive full credit.
Given the following inequality
[tex]\begin{gathered} \tan ^2(x)>\sqrt[]{5} \\ x\in\lbrack-\pi,\pi\rbrack \\ \end{gathered}[/tex]We need to check if x=0.981 is a solution.
This value is inside of the range, then, we just need to evaluate.
[tex]\tan ^2(0.981)\approx2.2325919107[/tex]Calculating the square root of 5:
[tex]\sqrt[]{5}\approx2.2360679775[/tex]From this, we know that the statement is false, because
[tex]\tan ^2(0.981)<\sqrt[]{5}[/tex]1. The sliders for y = ax + b have been set to create the following graph. What are possible values for a and b?
The slope of the line is m = 2 and the y-intercept b = 2
Therefore, the equation for the graph is
[tex]y=-2|x|+2[/tex]meaning a = -2 and b = 2.
(The negative sign in front of the absolute value drags the graph below the y = 0 )
Which angle is coterminal to 128°?A. -52°B. 308C. 232°D. 488°
The coterminal of angle with measure x is x + 360 degrees
Example:
If x = 30 degrees, then
The coterminal of x is 30 + 360 = 390 degrees
The coterminal of 128 degrees is 128 + 360 = 488 degrees
Then the answer is D
PLS HELP ASAP I WILL GIVE BRAINLIEST
Answer: I think the answer is [tex]\frac{2/3}{1}\\[/tex] and [tex]\frac{3}{1}[/tex]
Step-by-step explanation: I hope this helps. Correct me if I am wrong.
Following figure shows ABC with silencer the nearest 10th find AB in ABC
We have to find the length of AB.
We can use the Law of sines the tell us that the quotient between the sine of an angle and the length of the opposite side is constant for each of the three angles.
So we can write:
[tex]\begin{gathered} \frac{\sin(A)}{CB}=\frac{\sin(C)}{AB} \\ \frac{\sin(71\degree)}{6}=\frac{\sin(48\degree)}{AB} \\ AB=\frac{6\cdot\sin(48\degree)}{\sin(71\degree)} \\ AB\approx\frac{6\cdot0.743}{0.946} \\ AB\approx4.7 \end{gathered}[/tex]Answer: AB = 4.7
For the function f(x). describe, in words, the effects of each variable alb,h,k on the graph of a*f(bx+h)+k
Answer:
a: a produces vertical stretch
b: b produces a horizontal stretch
h: h produces a translation to the left of the X-axis
k: k produces a translation on the new function upward of the Y-axis
Step-by-step explanation:
An intermediate function is produced by adding each variable in the following order:
1) f(x) to f(bx):
Effect:
the horizontal stretch of f(x) along the x-axis with stretch factor b
2) f(bx) to f(bx+h):
Effect:
translation of f(bx) to the left of the X-axis by h units
3) f(bx+h) to a*f(bx+h):
Effect:
vertical stretching of f(bx+h) by a factor equal to a
4) Finally, a*f(bx+h) to a*f(bx+h)+k:
Effect:
vertical translation of a*f(bx+h) by h units upwards along the Y-axis.
Blaise M.
What is the image of the point (-7,-3) after a rotation of 90° counterclockwise about the origin?
The new point after rotation of point (-7, -3) counterclockwise by 90 degrees will be ( 3, -7).
What is meant by coordinates?A pair of numbers that employ the horizontal and vertical distinctions from the two reference axes to represent a point's placement on a coordinate plane. typically expressed by the x-value and y-value pairs (x, y).
Coordinates are always written in the form of small brackets the first term will be x and the second term will be y.
Given: the Point A be (-7, -3)
After rotation, this point moves to a unique coordinate (x, y) which exists as point B
Let's say the origin is O
Slope of line segment AO = (-3-0)/(-7-0) = 3/7
Slope of line segment BO = (y - 0)/(x - 0) = y/x
Since both lines exist perpendicular to each other so
Slope AO × Slope BO = -1
3/7 × y/x = -1
⇒ 3y = -7x
If we observe the result then it will be clear that if we put x = 3 then y = -7 will be the new coordinate.
Therefore, the new point after rotation of point (-7, -3) counterclockwise by 90 degrees will be ( 3, -7).
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A is in the shape of a quarter circle of radius 15 cm.
B is in the shape of a circle.
A
15 cm
The area of A is 9 times the area of B.
Work out the radius of B.
B
Answer:
[tex]\frac{5}{2}[/tex] or 2.5cm
Step-by-step explanation:
Hello! Let's help you with your question here!
Let's start by working out what we know and what we need. So, we know that P is a circle and Q is the shape of a quarter circle with a radius of 20cm. The area of Q is 9 times the area of P and we must find the radius of P.
To start, we're looking for area, so we should at least start looking at the area of a circle, given radius, which is:
[tex]A=\pi r^2[/tex]
Now, we don't necessarily know r (radius) and the area either. However, we can try to use the quarter circle as our guide for the full circle. So, we want to find the area of the quarter circle, we can do that by using this formula!
[tex]A=\frac{1}{4} \pi r^2[/tex]
The reason why we put a [tex]\frac{1}{4}[/tex] at the front of [tex]\pi r^{2}[/tex] is because we're only solving for a quarter of a circle instead of the entire circle.
Now that we have our formula! We can calculate the area of the quarter circle as follows:
[tex]A=\frac{1}{4}\pi 15^2[/tex]
[tex]A=\frac{\pi 15^2}{4}[/tex] -We combine the fraction [tex]\frac{1}{4}[/tex] into the rest of the equation.
[tex]A=\frac{225\pi }{4}[/tex] - Evaluating [tex]15^2[/tex]
Now that we have the area of the quarter circle, we can now work on the full circle. What we know is that the area of A is 9 times of B, since we're finding the radius of B, we can essentially plug in the area and solve for the radius of the full circle. That would be as such:
[tex]A=9\pi r^2[/tex] -We're using the area of circle A to find the radius of B.
[tex]\frac{225\pi }{4} =9\pi r^2[/tex] - Plugging in the area of the quarter circle.
[tex]\frac{225\pi }{4}/9\pi =\frac{9\pi r^2}{9\pi }[/tex] - We divide [tex]9\pi[/tex] to get rid of it on the right side.
[tex]\frac{25}{4} =r^2[/tex] - When dividing by [tex]\pi[/tex], the numerator [tex]\pi[/tex] gets cancelled out.
[tex]\sqrt{\frac{25}{4} }=r[/tex] -We square root to get rid of the squared.
[tex]\frac{5}{2}=r[/tex] - Square rooted both numerator and denominator.
And there we have it! We finally get a radius of [tex]\frac{5}{2}[/tex] or 2.5cm.
3 ftFind the outer perimeter ofthis figure. Round youranswer to the nearesthundredth. Use 3.14 toapproximate .4 ft5 ft5 ftP = [ ? ] ftNotice that only half of the circle is included in the figure!Enter
Perimeter = sum of outer lengths
Lenght of the triangle sides = 5ft
perimeter of a semicircle = π d; half = π d / 2
5 ft + 5ft + π r
5 + 5 + (3.14*3) = 19.42 ft
How much will the account be worth in 46 months?
In the question we are given the following parameters
Principal = $5100
Rate = 16.87% compounded semi-annually
Time = 46 months = 3yrs 10 months = 3 5/6 years
Explanation
We can solve the question using the formula below
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]"nt" is the number of months the principal accrues interest twice a year.
Therefore we have;
[tex]\begin{gathered} A=5100(1+\frac{16.87\div100}{2})^{\frac{23}{6}\times2} \\ A=5100(1+0.08435)^{\frac{23}{3}} \\ A=5100(1.08435)^{\frac{23}{3}} \\ A=9488.62 \end{gathered}[/tex]Answer:$9488.62
I need help with his practice problems from my ACT prep guidePlease show your work in steps
Answer:
[tex]-\sqrt[]{6}+1[/tex]Explanation:
Given the below expression;
[tex]\frac{\tan(-\frac{2\pi}{3})}{\sin(\frac{7\pi}{4})}-\sec (-\pi)[/tex]Recall that;
[tex]\begin{gathered} \sec x=\frac{1}{\cos x} \\ \sin x=\cos (\frac{\pi}{2}-x) \end{gathered}[/tex]So we can rewrite the expression as;
[tex]\begin{gathered} \frac{\tan(-\frac{2\pi}{3})}{\cos(\pi-\frac{7\pi}{4})}-\frac{1}{\cos(-\pi)} \\ \frac{\tan(-\frac{2\pi}{3})}{\cos(-\frac{5\pi}{4})}-\frac{1}{\cos(-\pi)} \end{gathered}[/tex]Also, recall that;
[tex]\begin{gathered} \cos (-x)=\cos x \\ \tan (-x)=-\tan x \end{gathered}[/tex]So we'll have;
[tex]\frac{-\tan (\frac{2\pi}{3})}{\cos (\frac{5\pi}{4})}-\frac{1}{\cos (\pi)}[/tex]From the Unit circle, we have that;
[tex]\begin{gathered} \cos \pi=-1 \\ \cos (\frac{5\pi}{4})=\frac{-\sqrt[]{2}}{2} \\ \tan (\frac{2\pi}{3})=-\sqrt[]{3} \end{gathered}[/tex]Substituting the above values into the expression and simplifying, we'll have;
[tex]\begin{gathered} \frac{-(-\sqrt[]{3})}{\frac{-\sqrt[]{2}}{2}}-\frac{1}{-1}=\frac{\sqrt[]{3}}{\frac{-\sqrt[]{2}}{2}}+1=-\frac{2\sqrt[]{3}\sqrt[]{2}}{\sqrt[]{2}\cdot\sqrt[]{2}}+1 \\ =-\sqrt[]{6}+1 \end{gathered}[/tex]on a trip of 2,300 miles, a missionary went 9 times as far by plane as by car. How for did the missionary travel by plane
Let the trip by car be c and the trip by plane be p.
The missionary travelled 9 times as far by plane as he did by car. This means if his trip by car is modelled by c, then the trip by plane would be 9c.
Hence, knowing that the entire trip of 2300 miles is by plane and by car;
[tex]\begin{gathered} c+p=2300 \\ \text{When p=9c, then} \\ c+9c=2300 \\ 10c=2300 \\ \text{Divide both sides by 10} \\ c=230 \\ \text{Therefore, his trip by plane would be derived as;} \\ c+p=2300 \\ 230+p=2300 \\ \text{Subtract 230from both sides} \\ p=2070 \end{gathered}[/tex]What is the least common denominator of 1/20 and 7/50
Considering the given fractions
[tex]\frac{1}{20};\frac{7}{50}[/tex]You have to find the least common denominator between the denominators "20" and "50"
For these values, the least common denominator is the least common multiple between both values:
[tex]20\cdot50=100[/tex]So, the least common denominator is 100.
I need help finding the passing adjusted grade of 70A=10R^1/2
Given:
Passing grade = 70
Formula for adjusted grade, A:
[tex]A=10R^{\frac{1}{2}}[/tex]Given a passing adjusted grade of 70, let's find the raw score, R.
To solve for R, substitute 70 for A and solve for R.
We have:
[tex]\begin{gathered} 70=10R^{\frac{1}{2}} \\ \end{gathered}[/tex]Divide both sides by 10:
[tex]\begin{gathered} \frac{70}{10}=\frac{10R^{\frac{1}{2}}}{10} \\ \\ 7=R^{\frac{1}{2}} \end{gathered}[/tex]Take the square of both sides:
[tex]\begin{gathered} 7^2=(R^{\frac{1}{2}})^2 \\ \\ 7^2=R^{\frac{1}{2}\times2} \\ \\ 49=R^1 \\ \\ 49=R \\ \\ R=49 \end{gathered}[/tex]Therefore, the raw score a student would need to have a passing adjusted grade of 70 is 49
ANSWER:
49
the mean monthly water bill for 82 residents in a local apartment complex is 137 dollars. what is the best point estimate for the mean monthly water bill for all residents of the local apartmemt complex?
From the information given, the mean monthly water bill for 82 residents in a local apartment complex is 137 dollars. The best estimate for the mean monthly water bill is the sample mean. Since 137 dollars is the sample mean, the correct answer is 137
the price of a lounge chair is $140 plus 7.5% sales tax.what is the sales tax on the lunge chair in dollors and cents
Given that the price is $140 , and the tax rate is 7.5% (0.075 in decimal form)
we can find the amount in taxes by the product :
0.075 times 140
0.075 * 140 = 10.5
so $10.5 is the amount to be paid in taxes
[tex]undefined[/tex]Hello! I think I'm overthinking this. Could you please help me decipher?
A scatter plot uses dots to represent values for two different values
(16,15)
(20,12)
(14,20)
(15,18)
(19,14)
(18,21)
Where the x value is boys and the y value is girls
what should be done to solve the following e q u a t i o n x + 8 equals 4
we have the equation
x+8=14
step 1
subtract 8 both sides
x+8-8=14-8
x=6
therefore the answer is the last option
HELP PLEASEEEEE!!!!!!
A horizontal line with evenly spaced numerical increments is referred to as a number line. How the number on the line can be answered depends on the numbers present. The use of the number is determined by the question that it corresponds to, such as when graphing a point.
The visual depiction of numbers, such as fractions, integers, and whole numbers, spread out uniformly along a single horizontal line is known as a number line. A number line can be used as a tool for operations like addition and subtraction as well as comparison and sorting of numbers.
Given:
As from the Figure we have
-1 3/4 = -7/4 = -1.75, which is represented by point 1 on the number line.
and, 14/8 = 1.75, which is represented by point 7 on the number line.
and, 1.125, which is represented by point 6 on the number line.
and, -0.875, which is represented by point 4 on the number line.
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What’s the volume and surface area of the object shown ?
Volume of object = 42 cubic cm
Surface area of object = 96 square cm
Explanations:The given figure is a triangular prism.The formula for calculating its volume is expressed as:
[tex]volume\text{ }of\text{ prism}=BH[/tex]where:
B is the base area
H is the height of prism
[tex]\begin{gathered} volume\text{ of }prism=(\frac{1}{2}\times4\times3)\times7 \\ volume\text{ of }prism=6\times7 \\ volume\text{ of }prism=42cm^3 \end{gathered}[/tex]Determine the surface area of the prism
The surface area if the sum of all the faces of the prism.The faces consists of 3 rectangles and 2 triangles. The surface area is calculated as:
[tex]\begin{gathered} Surface\text{ area}=2(0.5\times3\times4)+(7\times4)+(3\times7)+(5\times7) \\ Surface\text{ area}=12cm^2+28cm^2+21cm^2+35cm^2 \\ Surface\text{ area}=96cm^2 \end{gathered}[/tex]Hence the surface area of the object shown is 96 square cm
1.) You are buying flower bundles and have
$24 to spend. Rose bundles cost $4. Tulip bundles
cost $6. Write an equation to describe how many
types of each kind of bundle you can buy.
Answer:
[tex]4r+6t \leq 24[/tex]
Step-by-step explanation:
The cost of money spent on a rose bundle can be represented by 4r, where 4 is the cost of one rose bundle and r is the number of rose bundles purchased.
The cost of money spent on a tulip bundle can be represented by 6t, where 6 is the cost of one tulip bundle and t is the number of rose bundles purchased.
The amount spent on rose bundles added to the amount spent on tulip bundles must be equal to or less than $24, since that's all you have to spend. This can be represented using this equation:
[tex]4r + 6t \leq 24[/tex]
:)
help meee pleaseeee pleasee
Answer:
Step-by-step explanation:
A company plans a major investment and theamount of profit is uncertain, but researchersgive the following estimate for the distribution.1.5210Profit(inmillions)Probability0.10.20.40.20.1What is the expected value of the profit?[?] million dollars
The expected value is the return you expect from some kind of investment/action.
When we are presented with probabilty of an action, we can take the expected value of the whole table [investment] by taking the sum of the products of probability and the action.
Here, we want products of "probability" and "profit". Then we sum it. Shown below:
[tex]\begin{gathered} E=(0.1)(1)+(0.2)(1.5)+(0.4)(2)+(0.2)(4)+(0.1)(10) \\ E=3 \end{gathered}[/tex]Expected value of profit = 3 million dollarsIn general, what points can have coordinates reversed and still have the same location?Choose the correct answer below.O the points with x-coordinates 0o the points with y-coordinates 0o the points with the same x- and y-coordinatesO the points with opposite coordinates
SOLUTION
The Point of a co-ordinate is always written as
[tex](x,y)[/tex]Giving a point
[tex]\begin{gathered} A(x,y) \\ \text{if the coordinates of x and y are the same } \end{gathered}[/tex]For instance x=2 and y=2, the point will be
[tex](2,2)[/tex]If the coordinate of x and y are reversed, the point will remain the same
Hence
the points with the same x- and y-coordinates will give the same location if the coordinate is reversed.
Therefore The Third option is correct (c)
a museum wants to use equal rows to arrange the African baskets. which list shows all the different possible arrangements so that all the rows have the same number. Assume that an arrangement such as 4 x 20 is the same as 20 x 4.
Answer:
(B)1 x 80,2x 40,4 x 20,5 x 16,8 x 10
Explanation:
The number of African Baskets = 80
The list of all possible arrangements so that all the rows have the same number will be a list that contains all the positive product of factors of 80.
Factors of 80 are: 1,2,4,5,8, 10, 16,20,40,80
The list is, therefore:
[tex]1\times80,2\times40,4\times20,5\times16,8\times10[/tex]The correct choice is B.
e costs 7 dollars. Lamar buys p pounds. Write an equation to represent the total00XХ$?
Given:
A pound of chocolate costs 7 dollars.
To find:
The equation represents the total cost c for buying p pounds of chocolate.
Solution:
It is given that a pound of chocolate costs 7 dollars. So,
[tex]\begin{gathered} 1\text{ pound}=7\text{ dollars} \\ 1\times p\text{ pounds}=7\times p\text{ dollars} \\ p\text{ pounds}=7p\text{ dollars} \end{gathered}[/tex]Since the cost of p pounds of chocolate is c. So,
[tex]c=7p[/tex]Thus, the answer is c = 7p.
I need help with this practice problem solving It asks to divide
ANSWER
[tex]-\frac{5}{13}-\frac{14i}{13}[/tex]EXPLANATION
We want to divide the given complex fraction:
[tex]\frac{4+i}{-2+3i}[/tex]To do this, we have to rationalize the denominator of the fraction by multiplying the given fraction by another fraction made up of the conjugate of the denominator of the given fraction:
[tex]\frac{4+i}{-2+3i}\cdot\frac{-2-3i}{-2-3i}[/tex]Simplifying this, we have:
[tex]\begin{gathered} \frac{(4+i)(-2-3i)}{(-2+3i)(-2-3i)} \\ \Rightarrow\frac{-8-12i-2i+3}{4+6i-6i+9} \\ \frac{-8+3-12i-2i}{13}=\frac{-5-14i}{13} \\ \Rightarrow-\frac{5}{13}-\frac{14i}{13} \end{gathered}[/tex]That is the solution of the division.
Please help and answer this question ASAP! :)
Answer:
Odd, Even, Even, Neither=========================
The difference between odd and even functions is that:
f(-x) = f(x) for even functions,f(-x) = - f(x) for odd functions.Let's test this property for the given functions.
Function f(x)f(-4) = - f(4) = 8 and f(-2) = - f(2) = 1, so this is an odd functionFunction g(x)g(4) = g(-4) = -4 and g(2) = g(-2) = 2, so this is an even functionFunction j(x)j(2) = j(-2) = 2 and j(1) = (j-1) = - 4, so this is an even functionFunction k(x)k(-4) = 9, k(4) = 1 and k(-2) = 4, k(2) = 0, since each value is different this is neither odd nor even functionA squirrel is perched in a tree 50 feet above sea level. Directly below the squirrel, a bird is flying 17 feet above sea level. Directly below the bird is a trout, swimming 23 feet below seal level.how far apart are the squirrel and bird?
Solution
We can do the following operation_
17-50 = -33 ft
And that represent the distance between te heron and the squirrel
And since the actual height is -23 ft
Then the answer would be given by:
17 -(-23) = 40 ft
The distance from the squirrel and the bird is 40 ft
Drag the measurements to the containers to show equal length
The measurements that show equal length exists 15 yd and 540 in, 195 ft and 2340 in, 5280 yd and 15840 ft
What is meant by measurements?The fundamental idea in the study of science and mathematics is measurement. The qualities of an object or event can be quantified so that we can compare them to those of other objects or occurrences. When discussing the division of a quantity, measurement is the word that is used the most frequently.
An equation exists an expression that indicates the relationship between two or more numbers and variables.
1 ft = 12 in; 1 yd = 3 ft and 1 yd = 36 in.
Hence:
15 yd = 15 yd × 36 in per yd = 540 in
195 ft = 195 ft × 12 in per ft = 2340 in
5280 yd = 5280 yd * 3 ft per yd = 15840 ft
The measurements that show equal length exists 15 yd and 540 in, 195 ft and 2340 in, 5280 yd and 15840 ft.
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